Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
Correct Answer
$10115
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5950 × 7% × 10
= $5950 ×7/100 × 10
= 5950 × 7 × 10/100
= 41650 × 10/100
= 416500/100
= $4165
Thus, Simple Interest = $4165
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $4165
= $10115
Thus, Amount to be paid = $10115 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5950
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 7% × 10)
= $5950 + ($5950 ×7/100 × 10)
= $5950 + (5950 × 7 × 10/100)
= $5950 + (41650 × 10/100)
= $5950 + (416500/100)
= $5950 + $4165 = $10115
Thus, Amount (A) to be paid = $10115 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5950, the simple interest in 1 year
= 7/100 × 5950
= 7 × 5950/100
= 41650/100 = $416.5
Thus, simple interest for 1 year = $416.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $416.5 × 10 = $4165
Thus, Simple Interest (SI) = $4165
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $4165
= $10115
Thus, Amount to be paid = $10115 Answer
Similar Questions
(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(4) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.